Equation 1 · Part 6 · The Physical Plant: Power, Cooling, and Networks in an AI Datacenter

Volume flow rate

\dot{Q} = \dot{m}\,c_p\,\Delta T = \rho\,\dot{V}\,c_p\,\Delta T,

\dot{V}

What this part means

The volume of fluid passing through the loop each second. Its SI unit is cubic metres per second. Multiplying it by density gives the mass flow rate.

Its job in the formula

V̇ has a dot, marking the rate of change of the underlying indexed quantity with respect to the article’s time variable.

Full expressionVolume flow rateArticle meaning

The passage around this formula

The rate at which a fluid stream removes heat is $\dot{Q} = \dot{m}\,c_p\,\Delta T = \rho\,\dot{V}\,c_p\,\Delta T$ . with mass flow $\dot{m}$ , specific heat capacity $c_p$ , and the temperature rise $\Delta$ T across the load. What matters for a datacenter is not $c_p$ per kilogram but the volumetric heat capacity $\rho$ $c_p$ , because the room has to physically contain the flow.

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Learn the underlying idea

Units describe how a quantity is measured. A valid physical equation must combine compatible dimensions.

Open the illustrated units and dimensions: a formula’s consistency check guide →

See this notation across published equations →

Sources cited in the article section

[4] Emergence and Expansion of Liquid Cooling in Mainstream Data Centers ↗

These citations provide research context; check each source for the exact claim it supports.